Linear Matrix Inequality Approach Research Articles

Actuator fault estimation in wind turbine using a modified sliding mode observer based on Linear Matrix Inequality approach

Actuator fault estimation in wind turbine using a modified sliding mode observer based on Linear Matrix Inequality approach

Learning-Based Control of Autonomous Vehicles Using an Adaptive Neuro-Fuzzy Inference System and the Linear Matrix Inequality Approach.

This paper proposes a learning-based control approach for autonomous vehicles. An explicit Takagi-Sugeno (TS) controller is learned using input and output data from a preexisting controller, employing the Adaptive Neuro-Fuzzy Inference System (ANFIS) algorithm. At the same time, the vehicle model is identified in the TS model form for closed-loop stability assessment using Lyapunov theory and LMIs. The proposed approach is applied to learn the control law from an MPC controller, thus avoiding the use of online optimization. This reduces the computational burden of the control loop and facilitates real-time implementation. Finally, the proposed approach is assessed through simulation using a small-scale autonomous racing car.

Reliability-based anti-disturbance control for systems with parametric stochastic uncertainty: A probabilistic LMI approach

We propose a reliability-based anti-disturbance control (RADC) method for systems with parametric stochastic uncertainty based on the linear matrix inequality (LMI) and the limit state function. Differing from the existing anti-disturbance control, the parametric stochastic uncertainty is considered in both the concerned system and the exogenous disturbance system. With this consideration, the condition for system stability and performance robustness is described by a stochastic LMI which holds with a certain probability (reliability). Through the limit state function method, the stochastic LMI is subtly transformed into two probabilistic LMIs for two different cases. The proposed probabilistic LMIs contain two probabilistic parameters of reliability indexes that quantify the effect of parametric stochastic uncertainty. At different prescribed reliability indexes, controllers with different reliability can be flexibly and reliably designed. Two illustrative examples with Monte-Carlo verification are presented to demonstrate the feasibility and effectiveness of the proposed RADC method.

New LMI approach to [formula omitted] control of discrete-time singular systems

This article studies the problem of feedback H∞ control for discrete-time singular system. The objective is to design the controller to make the closed-loop system admissible and satisfy the specified H∞ performance. Firstly, the admissibility of the closed-loop system is analyzed via the Lyapunov function and linear matrix inequality (LMI) method, the admissibility condition of the singular system with H∞ performance is given. Then, applying a useful matrix inequality lemma, the controller design condition for discrete-time singular system is shown by a LMI. Specially, the benefit of the proposed design result is their less conservatism, the validity of the viewpoint is proposed by numeric illustrations.

Finite-Time H∞ Controllers Design for Stochastic Time-Delay Markovian Jump Systems with Partly Unknown Transition Probabilities.

This paper concentrates on the finite-time H∞ control problem for a type of stochastic discrete-time Markovian jump systems, characterized by time-delay and partly unknown transition probabilities. Initially, a stochastic finite-time (SFT) H∞ state feedback controller and an SFT H∞ observer-based state feedback controller are constructed to realize the closed-loop control of systems. Then, based on the Lyapunov-Krasovskii functional (LKF) method, some sufficient conditions are established to guarantee that closed-loop systems (CLSs) satisfy SFT boundedness and SFT H∞ boundedness. Furthermore, the controller gains are obtained with the use of the linear matrix inequality (LMI) approach. In the end, numerical examples reveal the reasonableness and effectiveness of the proposed designing schemes.

New Robust Model for Stability and H∞ Analysis for Interconnected Embedded Systems

This paper presents a novel approach to analyzing the robust stability of interconnected embedded systems. The paper starts by discussing the challenges associated with designing stable and robust embedded systems, particularly in the context of interconnected systems. The proposed approach combines the H∞ control theory with a new model for interconnected embedded systems, which takes into account the effects of communication delays and data losses. The paper provides a detailed mathematical analysis of the new model and presents several theorems and proofs related to its stability. The effectiveness of the proposed approach is demonstrated through several practical examples, including a networked control system and a distributed sensor network. The paper also discusses the limitations of the proposed approach and suggests several directions for future research. The proposed filter design method establishes a sufficient condition for the asymptotic stability of the error system and the satisfaction of a predefined H∞ performance index for time-invariant bounded uncertain parameters. This is achieved through the use of the strict linear matrix inequalities (LMI) approach and projection lemma. The design is formulated in terms of linear matrix inequalities (LMI). Numerical examples are provided to demonstrate the effectiveness of the proposed filter design methods.

Robust EMPC-Based Frequency-Adaptive Grid Voltage Sensorless Control for an LCL-Filtered Grid-Connected Inverter

A robust explicit model predictive control (EMPC)-based frequency-adaptive grid voltage sensorless control is developed for a grid-connected inverter (GCI) via a linear matrix inequality (LMI) approach under the model parametric uncertainties as well as distorted and imbalanced grid voltages. In order to ensure the quality of grid currents injected into the utility grid even when the system model parameters vary, the proposed control scheme is accomplished by an enhanced prediction model rather than the conventional prediction model obtained by fixed parameters. Furthermore, an LMI-based observer is integrated with the disturbance observer to improve the reference tracking performance and to reject disturbances. The proposed observer is employed for the grid frequency-adaptive control without the need for grid voltage sensors. The proposed current controller and observer employ the LMI scheme to maintain a stable and robust operation of the GCI. The discrete-time frequency response and pole-zero map analyses are utilized to examine the system performance including the stability and robustness against parametric uncertainties. Comprehensive simulation and experimental tests as well as theoretical analyses clearly validate the robustness of the proposed control scheme under various harsh test conditions with non-ideal and unexpected grid and system parametric uncertainties.

Sampled-Data Cooperative Adaptive Cruise Control for String-Stable Vehicle Platooning with Communication Delays: A Linear Matrix Inequality Approach

This study aims to propose a sampled-data control technique, utilizing a linear matrix inequality (LMI) approach, to achieve string-stable vehicle platooning in a cooperative adaptive cruise control (CACC) system with communication delays. To do this, a decentralized sampled-data controller design technique that combines one controller using sensor measurements and another one utilizing vehicle-to-vehicle (V2V) communication, ensuring both individual and string stability, is proposed first. Next, a memory sampled-data control (MSC) approach is presented to account for transmission delays in V2V communication. Additionally, an improved Lyapunov–Krasovskii functional (LKF) is presented to improve computational complexity and sampling performance. The design conditions are formulated as linear matrix inequalities (LMIs) in the time domain, facilitating efficient stability analysis and optimization. Finally, vehicle platooning simulations are provided to validate the effectiveness and feasibility of the proposed technique.

Stabilising control for impulsive systems

This paper is aimed at stabilising control for impulsive systems via the state feedback. Firstly, stability analysis for the closed-loop system is conducted using a Lyapunov-like functional (LLK) that is not necessarily continuous nor positive definite. Built on two subintervals of the impulsive interval being separated by the current instant, a concrete LLK is constructed by introducing multiple integrals of the state and cross terms among the integrals, the state and impulsive states. Integral equations of the impulsive system are exploited and high-order integral inequalities are taken when estimating the derivative of the LLK. New stability results with interval dwell-time, maximal dwell-time or minimal dwell-time are obtained. Secondly, based on the stability results the stabilising control problem is solved via linear matrix inequality approach. Finally, numerical examples illustrate that the stability results are less conservative and the control for impulsive systems is valid.

A linear matrix inequality approach to optimal reset control design for a class of nonlinear systems

AbstractIn this article, the problem of the optimal reset control design for Lipschitz nonlinear systems is addressed. The reset controller includes a base linear controller and a reset law that enforces resets to the controller states. The reset law design is strongly dependent on the appropriate design of the base controller. For this reason, in this article, the base controller and reset law are simultaneously designed. More precisely, an optimal dynamic output feedback is considered as the base controller which minimizes the upper bound of a quadratic performance index, and a reset law is used to improve the transient response of the closed‐loop system. This design is done in a full offline procedure. The problem is transformed into a set of linear matrix inequalities (LMIs), and the reset controller is obtained by solving an offline LMI optimization problem. Finally, two examples are presented to illustrate the effectiveness and validity of the proposed method.

Sparse Structure Design for Stochastic Linear Systems via a Linear Matrix Inequality Approach

Sparse Structure Design for Stochastic Linear Systems via a Linear Matrix Inequality Approach

Optimal non-fragile control design for linear systems under amplitude and rate saturation: An LMI approach

In this paper, the problem of optimal non-fragile guaranteed cost control design for linear systems subject to input amplitude and rate saturation is addressed. Sufficient conditions for the existence of a non-fragile state feedback are obtained by Lyapunov stability theory. The designed controller not only guarantees the asymptotic stability of the overall closed-loop system with a minimum upper bound of a cost function, but also ensures the actuator saturation avoidance. This problem is transformed into an optimization problem with linear matrix inequality (LMI) constraints. The proposed method guarantees that the control input amplitude and rate remain within the allowable ranges and do not exceed the considered bounds. The simulation results illustrate the effectiveness and superiority of the proposed theoretical results.

Frequency-based multivariable control design with stability margin constraints: A linear matrix inequality approach

In this paper, a proportional–integral–derivative controller design problem for stable multivariable process is considered. A frequency-based control technique is formulated as a convex optimization problem with linear matrix inequality constraint. The multivariable proportional–integral–derivative controller is designed so that H∞ norm of the difference between the designed loop gain function and a desired one is minimized. Linear matrix inequality constraints on the stability margin guarantees designed loop stability. Process frequency domain data is used to solve the proposed optimization problem. Knowledge of the process parametric model is not necessary. The desired loop gain transfer function is defined from the reference complementary sensitivity function. Simulation results show the comparison between the proposed technique and technique from the literature. In these examples, the proposed technique resulted in stable closed-loops different from the others and in a reduction of the performance indices.

Stability and Stabilization for Delay Delta Fractional Order Systems: An LMI Approach

The well-known delta fractional calculus is widely used in system analysis and synthesis. However, the irregular stable region brings many unexpected difficulties and challenges. The simple linear matrix inequality (LMI) condition, especially α(1,2), is lacking. This brief constructs a circular region to approximate the true stable region. Afterwards, the sufficient conditions in terms of LMIs are derived. It is shown that the elaborated results are valid and effective.

An iterative output feedback controller-design strategy for energy-to-peak structural vibration control

ABSTRACT To address the issue of inadequate control effect resulting from the challenge of measuring state feedback information comprehensively, this paper proposes an iterative output feedback energy-to-peak control method that solely depends on partial external observation data. This paper presents the computational steps for achieving a suboptimal solution to the output feedback bilinear matrix inequality constrained problem using an iterative linear matrix inequality approach. The proposed method overcomes the challenge of numerically solving the optimization problem. The unknown variables in the output feedback linear matrix inequality optimization problem are transformed equivalently to obtain a new linear matrix inequality optimization problem. The numerical results of the two optimization problems are then used to iterate with each other and obtain a suboptimal solution. A comprehensive analysis was conducted on an 8-story building structure, utilizing state feedback, output feedback, and iterative output feedback energy-to-peak control techniques. The results of the study indicate that the proposed iterative output feedback energy-to-peak control approach efficiently reduces the displacement and acceleration response of the structure, exhibiting superior control effectiveness than both the state feedback and output feedback energy-to-peak control methods. The findings demonstrate the practicality and versatility of the suggested method.

Output tracking control design with anti-disturbance rejection for modified repetitive nonlinear control systems

ABSTRACTThis paper intends to analyse the disturbance rejection and output tracking control for a class of nonlinear control systems with disturbances. In this connection, we present a method that combines a proportional-integral observer and nonlinear-equivalent-input-disturbance estimator for superior disturbance rejection performance. Specifically, the nonlinear-equivalent-input-disturbance estimator comprises of equivalent-input-disturbance estimator and nonlinear feedback term, which is employed to estimate and reject the disturbances from the nonlinear system. Notably, the proportional-integral loop in the proportional-integral observer reduces the estimation inaccuracy of the nonlinear-equivalent-input-disturbance. Then the estimated disturbance is intertwined into the repetitive control input to compensate it efficiently. In order to obtain the required results, the proposed control system is converted into a two-dimensional modified repetitive control system to describe the learning and control actions. In particular, the proposed controller enables to adjust the gains directly to improve the learning and control performance and as a result, the tracking accuracy increases. Using a general Lyapunov–Krasovskii functional, singular value decomposition technique and linear matrix inequalities approach, a design algorithm for establishing proportional-integral observer and feedback gains is developed for the system under consideration. Finally, simulation results are given to illustrate the developed method's validity and superiority.

Boundary stabilisation of fractional reaction-diffusion systems with time-varying delays

This paper examines the boundary stabilisation results for time fractional-order reaction-diffusion systems involving with time-varying delays. The main goal is to design the boundary control for the system by proving the well-posedness of the kernel function using the backstepping method. An invertible Volterra integral transformation is used to convert the considered system into a stable target system. Different from the existing results, the stability results for fractional RDEs are discussed in the sense of the Lyapunov–Krasovskii theory and sufficient conditions are derived with the help of the linear matrix inequality (LMI) approach. Finally, to show the application of the results, the proposed conditions are numerically validated over a time fractional-order reaction-diffusion cellular neural network model.

Event-triggered robust model reference adaptive control for drag-free satellite

Aiming at the requirement of bounded disturbance suppression for low-frequency space gravitational wave detection satellite, a robust model reference adaptive drag-free control scheme is proposed in this paper via linear matrix inequalities (LMIs) approach. The multivariable model reference adaptive control (MRAC) scheme is applied to the drag-free control system with parameter uncertainties, which realizes the adaptive tracking to the reference state. The LMI system is established as an adaptive compensation term, which provides robustness against nonlinear disturbances. To reduce the communication burden of the actuation information and further save the total energies, an event-triggered mechanism (ETM) is introduced, with both the actuation inputs and the adaptive laws of the feedback gains updated only at the triggering time instants. The ultimately uniformly boundedness of the closed-loop signals is proved by Lyapunov analysis, with each system state convergence. From the feasibility analysis, Zeno behavior can be further proved to be strictly excluded. The numerical simulation verifies that the proposed scheme has efficient robustness to nonlinear disturbances with low energy cost, and achieves good effect in response to the requirements of space gravitational wave detection mission.

Consensus of nonlinear multiagent systems with mode‐dependent delay via stochastic sampled data under Markovian switching topologies

AbstractIn this article, we investigate the mean‐square consensus problem of multiagent systems with one leader and multiple followers. In consideration of the uncertain disturbance from external environment or internal change of system, the interaction topology and time‐varying delay switch randomly which are regulated by a time‐homogeneous Markovian chain. The distributed control protocol is designed based on the stochastic sampling information from its neighbors and the leader. Using stochastic Lyapunov theory and linear matrix inequality (LMI) approach, the sufficient condition is concluded to guarantee the mean‐square consensus. For the undirected topology case, a low‐dimensional LMI‐based consensus criterion is further derived based on the matrix diagonalization method. Finally, a numerical simulation is provided to demonstrate the reasonability of the theoretical results.

An LMI adaptive-barrier function global sliding mode control of uncertain nonlinear systems with input saturation

This paper proposes a barrier function-based adaptive control strategy with a nonlinear sliding surface for a class of uncertain dynamic systems with input saturation. Its main objectives are to ensure robustness to parametric and non-parametric uncertainties whilst eliminating the reaching phase. A global nonlinear switching surface is defined and an adaptive barrier function sliding mode control approach is derived. The barrier strategy is adopted to ensure the convergence of the states to the desired values without overestimating the control gains. System stability is analyzed using the Lyapunov stability theory. The control parameters are obtained using the linear matrix inequality (LMI) approach. The control law is designed to remove the reaching phase. The effectiveness of the proposed approach was validated using a simulation study. The proposed control approach can easily be implemented to various nonlinear uncertain systems.